Poisson cohomology of 3D Lie algebras
Douwe Hoekstra, Florian Zeiser
TL;DR
This paper computes the Poisson cohomology for all linear Poisson structures in three dimensions by analyzing various 3D Lie algebras, expanding the understanding of their algebraic and geometric properties.
Contribution
It provides a complete classification of Poisson cohomology for all 3D Lie algebra-based structures, filling a gap in the existing literature.
Findings
Poisson cohomology computed for all 3D Lie algebras
Classification-based approach to Poisson structures
Enhanced understanding of 3D linear Poisson structures
Abstract
We compute the Poisson cohomology associated with several three dimensional Lie algebras. Together with existing results and the classification of three dimensional Lie algebras, this provides the Poisson cohomology of all linear Poisson structures in dimension 3.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Ophthalmology and Eye Disorders